Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: *rf_harvest_est_nm_wt_thru2023_3e+05__2025-06-04* (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9599

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

##  [1] "re_dsr"       "re_pelagic"   "p_dsr"        "Hd_ayg"       "beta1_pH"    
##  [6] "p_pelagic"    "Hp_ay"        "Hb_ay"        "re_pH"        "beta0_pH"    
## [11] "re_yellow"    "Hd_ay"        "Hp_ayg"       "Hb_ayg"       "Hy_ay"       
## [16] "Tp_ay"        "Hdnye_ayg"    "mu_beta2_pH"  "Tb_ay"        "Rb_ay"       
## [21] "Rb_ay_mort"   "Rp_ay"        "Rp_ay_mort"   "Rb_ayg"       "Rb_ayg_mort" 
## [26] "Rp_ayg"       "Rp_ayg_mort"  "beta2_pH"     "R_ayg"        "R_ay"        
## [31] "Bb_ay"        "Bb_ayg"       "Tb_ayg"       "Tp_ayg"       "Bp_ay"       
## [36] "Bp_ayg"       "Rb_ayu"       "Rb_ayu_mort"  "Rp_ayu_mort"  "Rp_ayu"      
## [41] "Bb_ayu"       "Bp_ayu"       "Tp_ayu"       "Tb_ayu"       "R_ayu"       
## [46] "Hy_ayg"       "Ry_ayu"       "Ry_ayu_mort"  "Ry_ayg"       "Ry_ayg_mort" 
## [51] "Ry_ay"        "Ry_ay_mort"   "Ro_ayu"       "Ro_ay"        "Ty_ayg"      
## [56] "pDSR_YE_ay"   "By_ayg"       "Ro_ayg"       "p_yellow"     "pDSR_YE_ayu" 
## [61] "Ty_ay"        "By_ay"        "Ho_ay"        "Tdnye_ayg"    "Hb_ayu"      
## [66] "Hp_ayu"       "pH"           "Bdnye_ayg"    "tau_beta4_pH" "Ho_ayg"      
## [71] "Ty_ayu"       "Tdnye_ay"     "Hy_ayu"       "Ho_ayu"       "Hdnye_ay"    
## [76] "Bdnye_ay"     "By_ayu"       "tau_beta0_pH" "beta3_pH"     "H_ayu"       
## [81] "Rs_ayu"       "Rs_ayu_mort"  "Ts_ay"        "beta4_pH"     "Hs_ay"       
## [86] "pDSR_YE_ayg"  "Ts_ayg"       "Rd_ayg"       "Hs_ayg"       "H_ay"        
## [91] "Rs_ay_mort"

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta0_pelagic 3 1.897562 beta1_pelagic 5 1.621379 beta3_yellow 2 1.451039 beta3_pelagic 2 1.419504 beta0_yellow 2 1.415607 beta2_yellow 4 1.374961 beta1_yellow 2 1.350898

parameter n badRhat_avg beta2_pelagic 5 1.299429 sd_comp 1 1.268725 beta1_pH 9 1.266105 beta0_pH 4 1.214958 tau_beta0_pH 1 1.157034 beta2_pH 8 1.151706 beta3_pH 1 1.149030

Table 2. Summary of unconverged major parameters by area

Parameter	CI	NG	PWSI	PWSO	BSAI	SOKO2SAP	WKMA	afognak	eastside	northeast	CSEO	EWYKT	NSEI	NSEO	SSEI	SSEO
beta0_pH	0	0	0	0	0	0	1	0	0	0	2	0	0	0	1	0
beta0_pH	0	0	0	0	0	0	1	0	0	0	1	0	0	0	1	0
beta1_pH	0	0	1	1	1	1	1	0	0	1	2	0	0	0	1	0
beta1_pH	0	0	1	1	1	1	1	0	0	1	1	0	0	0	1	0
beta2_pH	2	1	1	1	0	0	1	1	0	1	0	0	0	0	0	0
beta2_pH	1	1	1	1	0	0	1	1	0	1	0	0	0	0	0	0
beta3_pH	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
beta3_pH	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
beta4_pH	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Bp_ay	0	0	0	0	0	0	0	0	0	0	21	9	0	3	0	1
Bp_ayg	0	0	0	0	0	0	0	0	0	0	19	11	0	4	0	1
Bp_ayu	0	0	0	0	0	0	0	0	0	0	16	1	0	1	1	0
H_ay	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
H_ayu	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
Hb_ay	0	0	0	7	0	0	0	0	0	0	21	0	0	0	0	0
Hb_ayg	0	0	0	5	0	0	0	0	0	0	21	0	0	0	0	0
Hb_ayu	0	0	0	1	0	0	0	2	0	0	18	0	0	0	0	0
Hd_ay	0	0	0	0	0	0	0	0	0	0	21	0	0	0	16	0
Hd_ayg	0	0	0	0	0	0	0	0	0	0	19	0	0	0	10	0
Hdnye_ay	0	0	0	0	0	0	0	0	0	0	11	0	0	0	1	0
Hdnye_ayg	0	0	0	0	0	0	0	0	0	0	6	0	0	0	8	0
Ho_ay	0	0	0	0	1	0	0	0	0	0	13	0	0	0	0	0
Ho_ayg	0	0	0	0	0	0	0	0	0	0	11	0	0	0	0	0
Ho_ayu	0	0	0	0	1	0	0	1	1	0	0	0	0	0	0	0
Hp_ay	0	0	0	9	0	0	0	0	0	0	21	0	0	0	0	0
Hp_ayg	0	0	0	5	0	0	0	0	0	0	21	0	0	0	0	0
Hp_ayu	0	0	0	1	0	0	0	1	0	0	18	0	0	0	0	0
Hs_ay	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
Hs_ayg	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
Hy_ay	0	0	0	0	1	0	0	1	0	0	21	0	0	0	0	0
Hy_ayg	0	0	0	0	0	0	0	0	0	0	18	0	0	0	0	0
Hy_ayu	0	0	0	0	1	0	0	1	0	0	2	0	0	0	0	0
mu_beta2_pH	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
p_dsr	0	0	0	0	0	0	0	0	0	0	0	29	0	0	61	0
p_pelagic	0	0	0	35	0	0	0	0	0	0	45	0	0	0	0	0
p_yellow	0	0	0	0	0	0	0	0	0	0	2	0	0	0	1	0
pDSR_YE_ay	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0
pDSR_YE_ayg	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
pDSR_YE_ayu	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0
pH	10	12	0	0	0	0	0	0	0	0	3	0	0	0	1	0
R_ay	11	7	11	9	7	9	11	9	8	8	13	12	1	9	2	3
R_ayg	11	6	13	11	7	14	11	10	9	11	13	12	1	8	1	4
R_ayu	2	3	2	2	6	7	5	4	5	2	10	3	0	2	1	0
Rb_ay	21	17	12	10	8	8	11	9	8	8	13	12	1	9	2	3
Rb_ay_mort	20	18	12	9	7	8	11	9	8	7	13	12	1	9	2	3
Rb_ayg	11	6	13	10	7	14	11	10	8	12	13	12	1	8	1	4
Rb_ayg_mort	11	6	13	10	7	14	11	10	8	12	13	12	1	8	1	4
Rb_ayu	13	16	4	4	6	6	7	5	7	2	13	4	1	5	1	0
Rb_ayu_mort	13	16	4	4	6	6	7	5	7	2	13	4	1	5	1	0
Rd_ayg	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
re_pelagic	0	0	0	9	0	0	0	0	0	0	32	0	2	0	0	0
re_pH	3	20	10	10	0	0	25	0	0	0	8	0	0	0	5	0
Ro_ay	1	0	0	0	20	12	2	1	1	0	0	0	0	0	0	0
Ro_ayg	1	0	0	0	2	1	0	0	3	0	0	0	0	0	0	0
Ro_ayu	1	0	0	0	20	12	2	1	0	0	0	0	0	0	0	0
Rp_ay	21	19	12	10	7	9	11	10	8	8	13	12	1	9	2	3
Rp_ay_mort	21	18	12	10	7	9	11	10	8	8	13	12	1	9	2	3
Rp_ayg	11	6	13	11	7	14	11	10	9	11	13	12	1	8	1	4
Rp_ayg_mort	11	6	13	11	7	14	11	10	9	11	13	12	1	8	1	4
Rp_ayu	11	16	5	4	6	7	7	4	7	2	13	4	1	5	1	0
Rp_ayu_mort	11	16	5	4	6	7	7	4	7	2	13	4	1	5	1	0
Rs_ay_mort	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0
Rs_ayu	0	0	0	0	0	0	0	0	0	0	0	6	0	0	0	0
Rs_ayu_mort	0	0	0	0	0	0	0	0	0	0	0	6	0	0	0	0
Ry_ay	0	0	0	0	9	2	1	1	1	0	0	0	0	0	0	0
Ry_ay_mort	0	0	0	0	9	2	1	1	1	0	0	0	0	0	0	0
Ry_ayg	0	0	0	0	4	1	0	1	0	0	0	0	0	0	0	0
Ry_ayg_mort	0	0	0	0	4	1	0	1	0	0	0	0	0	0	0	0
Ry_ayu	0	0	0	0	8	2	1	1	1	0	0	0	0	0	0	0
Ry_ayu_mort	0	0	0	0	8	2	1	1	1	0	0	0	0	0	0	0
tau_beta0_pH	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta0_pH	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta4_pH	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Tp_ay	4	0	3	6	2	5	6	6	6	4	21	9	0	3	0	1
Tp_ayg	5	0	6	5	5	9	7	6	7	5	21	11	0	4	0	2
Tp_ayu	0	0	0	1	1	4	1	0	3	0	16	1	0	1	1	0
beta0_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	0	0	0	0
beta0_yellow	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0
beta1_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	1	1	0	0
beta1_yellow	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0
beta2_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	1	1	0	0
beta2_yellow	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0
beta3_pelagic	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0
beta3_yellow	0	0	0	0	0	0	0	0	0	0	1	0	0	1	0	0
sd_comp	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.137	0.071	-0.265	-0.140	0.009
mu_bc_H[2]	-0.105	0.047	-0.187	-0.108	-0.004
mu_bc_H[3]	-0.438	0.069	-0.570	-0.440	-0.297
mu_bc_H[4]	-1.002	0.195	-1.390	-1.001	-0.625
mu_bc_H[5]	0.802	0.870	-0.209	0.634	2.827
mu_bc_H[6]	-2.195	0.321	-2.807	-2.207	-1.571
mu_bc_H[7]	-0.469	0.108	-0.685	-0.466	-0.266
mu_bc_H[8]	0.204	0.349	-0.386	0.173	1.010
mu_bc_H[9]	-0.297	0.134	-0.564	-0.293	-0.030
mu_bc_H[10]	-0.112	0.071	-0.242	-0.114	0.029
mu_bc_H[11]	-0.131	0.040	-0.211	-0.130	-0.054
mu_bc_H[12]	-0.262	0.106	-0.489	-0.257	-0.063
mu_bc_H[13]	-0.155	0.087	-0.332	-0.151	0.013
mu_bc_H[14]	-0.316	0.103	-0.528	-0.313	-0.126
mu_bc_H[15]	-0.354	0.051	-0.456	-0.354	-0.255
mu_bc_H[16]	-0.383	0.412	-1.133	-0.404	0.480
mu_bc_R[1]	1.351	0.149	1.060	1.351	1.646
mu_bc_R[2]	1.473	0.094	1.275	1.474	1.656
mu_bc_R[3]	1.409	0.145	1.112	1.411	1.683
mu_bc_R[4]	0.965	0.207	0.522	0.977	1.343
mu_bc_R[5]	1.310	0.495	0.332	1.304	2.284
mu_bc_R[6]	-1.462	0.495	-2.375	-1.477	-0.418
mu_bc_R[7]	0.442	0.199	0.025	0.451	0.799
mu_bc_R[8]	0.557	0.188	0.186	0.561	0.930
mu_bc_R[9]	0.370	0.210	-0.068	0.387	0.747
mu_bc_R[10]	1.351	0.175	0.984	1.356	1.674
mu_bc_R[11]	1.050	0.100	0.856	1.049	1.245
mu_bc_R[12]	0.835	0.212	0.422	0.830	1.248
mu_bc_R[13]	1.047	0.111	0.841	1.043	1.274
mu_bc_R[14]	0.909	0.145	0.624	0.910	1.184
mu_bc_R[15]	0.800	0.120	0.571	0.796	1.046
mu_bc_R[16]	1.111	0.130	0.856	1.111	1.367
tau_pH[1]	3.770	2.010	0.098	4.805	5.875
tau_pH[2]	1.969	0.230	1.542	1.956	2.450
tau_pH[3]	2.139	0.222	1.726	2.128	2.596
beta0_pH[1,1]	1.053	0.814	0.228	0.653	2.915
beta0_pH[2,1]	2.306	1.879	1.024	1.504	8.732
beta0_pH[3,1]	1.828	0.701	0.998	1.539	3.633
beta0_pH[4,1]	2.140	0.926	1.196	1.717	4.731
beta0_pH[5,1]	-0.331	0.993	-1.389	-0.701	2.341
beta0_pH[6,1]	-0.265	0.785	-1.462	-0.441	1.761
beta0_pH[7,1]	-0.059	1.032	-1.670	-0.312	2.458
beta0_pH[8,1]	-0.220	0.847	-1.230	-0.486	2.262
beta0_pH[9,1]	-0.200	0.889	-1.214	-0.505	2.100
beta0_pH[10,1]	0.757	0.874	-0.033	0.435	2.981
beta0_pH[11,1]	0.825	2.386	-0.601	-0.068	8.883
beta0_pH[12,1]	0.847	0.774	0.100	0.541	2.787
beta0_pH[13,1]	0.846	1.738	-0.235	0.077	6.397
beta0_pH[14,1]	0.223	1.051	-0.586	-0.221	3.169
beta0_pH[15,1]	0.902	1.937	-0.329	0.076	6.942
beta0_pH[16,1]	0.452	1.637	-0.905	-0.211	5.464
beta0_pH[1,2]	2.836	0.163	2.501	2.842	3.137
beta0_pH[2,2]	2.880	0.139	2.607	2.881	3.154
beta0_pH[3,2]	3.127	0.153	2.840	3.124	3.435
beta0_pH[4,2]	2.951	0.133	2.687	2.951	3.218
beta0_pH[5,2]	4.749	1.396	2.936	4.444	8.288
beta0_pH[6,2]	3.116	0.211	2.704	3.116	3.534
beta0_pH[7,2]	1.834	0.196	1.452	1.841	2.196
beta0_pH[8,2]	2.873	0.177	2.519	2.878	3.205
beta0_pH[9,2]	3.430	0.226	2.996	3.427	3.884
beta0_pH[10,2]	3.683	0.209	3.290	3.679	4.095
beta0_pH[11,2]	-4.861	0.311	-5.518	-4.839	-4.283
beta0_pH[12,2]	-4.741	0.374	-5.500	-4.732	-4.035
beta0_pH[13,2]	-4.552	0.404	-5.328	-4.567	-3.714
beta0_pH[14,2]	-5.578	0.471	-6.541	-5.556	-4.730
beta0_pH[15,2]	-4.301	0.337	-4.945	-4.308	-3.660
beta0_pH[16,2]	-4.856	0.389	-5.645	-4.843	-4.102
beta0_pH[1,3]	-0.259	0.765	-2.098	-0.155	0.935
beta0_pH[2,3]	2.192	0.164	1.883	2.192	2.519
beta0_pH[3,3]	2.527	0.148	2.233	2.529	2.817
beta0_pH[4,3]	2.967	0.159	2.646	2.964	3.278
beta0_pH[5,3]	1.963	1.343	0.303	1.661	5.284
beta0_pH[6,3]	0.964	0.509	-0.243	1.010	1.844
beta0_pH[7,3]	0.633	0.172	0.307	0.630	0.973
beta0_pH[8,3]	0.312	0.188	-0.054	0.310	0.682
beta0_pH[9,3]	-0.615	0.376	-1.527	-0.585	0.053
beta0_pH[10,3]	0.477	0.376	-0.441	0.525	1.084
beta0_pH[11,3]	-0.165	0.334	-0.822	-0.162	0.463
beta0_pH[12,3]	-0.841	0.347	-1.610	-0.809	-0.252
beta0_pH[13,3]	-0.192	0.337	-0.856	-0.183	0.442
beta0_pH[14,3]	-0.257	0.266	-0.777	-0.259	0.278
beta0_pH[15,3]	-0.727	0.350	-1.374	-0.723	-0.078
beta0_pH[16,3]	-0.410	0.302	-1.033	-0.393	0.129
beta1_pH[1,1]	2.156	1.405	0.000	2.881	3.656
beta1_pH[2,1]	1.476	1.000	0.000	1.963	2.658
beta1_pH[3,1]	1.396	0.960	0.000	1.792	2.697
beta1_pH[4,1]	1.649	1.089	0.000	2.168	2.934
beta1_pH[5,1]	1.817	0.919	0.000	2.120	2.988
beta1_pH[6,1]	2.824	1.682	0.000	3.090	5.939
beta1_pH[7,1]	2.054	1.349	0.000	2.212	5.047
beta1_pH[8,1]	2.893	1.638	0.000	3.288	5.554
beta1_pH[9,1]	1.835	0.951	0.000	2.144	3.066
beta1_pH[10,1]	2.065	1.269	0.000	2.158	6.376
beta1_pH[11,1]	3.091	1.552	0.000	3.279	6.863
beta1_pH[12,1]	2.083	0.989	0.000	2.498	3.017
beta1_pH[13,1]	2.345	1.114	0.000	2.846	3.328
beta1_pH[14,1]	2.764	1.253	0.000	3.300	3.796
beta1_pH[15,1]	2.002	0.974	0.000	2.397	2.954
beta1_pH[16,1]	3.120	1.482	0.000	3.635	5.017
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.004	0.062	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.002	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.679	0.355	6.014	6.663	7.396
beta1_pH[12,2]	6.391	0.430	5.606	6.374	7.279
beta1_pH[13,2]	6.918	0.440	6.023	6.926	7.788
beta1_pH[14,2]	7.216	0.495	6.322	7.195	8.223
beta1_pH[15,2]	6.771	0.369	6.074	6.753	7.498
beta1_pH[16,2]	7.431	0.426	6.583	7.431	8.289
beta1_pH[1,3]	4.835	1.620	2.356	4.610	8.233
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.543	5.066	0.690	2.758	10.956
beta1_pH[6,3]	3.076	3.750	0.439	2.571	8.950
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.744	0.341	2.074	2.747	3.406
beta1_pH[9,3]	2.733	0.440	1.969	2.705	3.725
beta1_pH[10,3]	2.893	0.459	2.138	2.845	4.015
beta1_pH[11,3]	2.730	0.405	1.977	2.714	3.543
beta1_pH[12,3]	4.079	0.432	3.303	4.059	5.005
beta1_pH[13,3]	1.744	0.348	1.081	1.735	2.411
beta1_pH[14,3]	2.491	0.335	1.834	2.481	3.155
beta1_pH[15,3]	2.012	0.357	1.315	2.003	2.634
beta1_pH[16,3]	1.792	0.318	1.220	1.774	2.471
beta2_pH[1,1]	-0.301	5.483	-14.795	0.452	12.213
beta2_pH[2,1]	-0.197	5.576	-14.799	0.502	11.926
beta2_pH[3,1]	-0.118	5.551	-14.783	0.525	12.585
beta2_pH[4,1]	-0.303	5.520	-14.153	0.436	12.123
beta2_pH[5,1]	1.256	1.723	-2.056	1.133	4.708
beta2_pH[6,1]	0.339	1.451	-1.822	0.184	3.984
beta2_pH[7,1]	0.888	14.707	0.000	0.000	0.319
beta2_pH[8,1]	0.360	1.494	-2.361	0.249	3.213
beta2_pH[9,1]	0.523	1.545	-1.758	0.386	3.887
beta2_pH[10,1]	0.577	1.446	-1.748	0.512	3.482
beta2_pH[11,1]	1.101	4.162	-5.931	0.724	13.301
beta2_pH[12,1]	1.571	4.303	-7.039	1.192	13.133
beta2_pH[13,1]	1.179	4.168	-6.794	0.759	12.506
beta2_pH[14,1]	1.220	4.199	-6.471	0.826	12.679
beta2_pH[15,1]	1.163	4.356	-6.871	0.766	12.664
beta2_pH[16,1]	0.824	4.280	-7.171	0.408	12.651
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.004	1.861	-7.114	-1.532	-0.033
beta2_pH[4,2]	-2.034	1.832	-6.738	-1.555	-0.033
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.465	4.291	-20.464	-8.493	-3.944
beta2_pH[12,2]	-8.067	4.869	-20.176	-7.180	-1.146
beta2_pH[13,2]	-7.956	4.974	-20.216	-6.868	-1.700
beta2_pH[14,2]	-8.391	4.642	-20.294	-7.313	-2.481
beta2_pH[15,2]	-9.220	4.372	-20.438	-8.160	-3.720
beta2_pH[16,2]	-9.468	4.315	-20.263	-8.427	-3.994
beta2_pH[1,3]	0.224	0.267	0.101	0.175	0.572
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	9.137	6.299	-0.043	8.188	23.336
beta2_pH[6,3]	9.204	6.124	0.240	8.190	23.239
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	10.141	5.745	1.995	9.204	24.011
beta2_pH[9,3]	9.072	6.198	0.547	8.124	23.557
beta2_pH[10,3]	8.543	6.427	0.501	7.487	23.013
beta2_pH[11,3]	-2.427	2.388	-9.581	-1.695	-0.573
beta2_pH[12,3]	-2.659	2.228	-8.953	-1.960	-0.953
beta2_pH[13,3]	-3.134	2.638	-10.748	-2.267	-0.704
beta2_pH[14,3]	-3.126	2.554	-10.447	-2.279	-0.893
beta2_pH[15,3]	-3.456	2.715	-11.237	-2.498	-1.002
beta2_pH[16,3]	-3.333	2.721	-10.969	-2.431	-0.891
beta3_pH[1,1]	34.185	5.102	19.504	35.688	42.558
beta3_pH[2,1]	32.507	4.881	19.535	33.446	42.760
beta3_pH[3,1]	32.498	4.849	19.415	33.477	43.145
beta3_pH[4,1]	31.825	4.867	19.006	33.400	37.827
beta3_pH[5,1]	28.437	3.853	20.652	27.563	40.185
beta3_pH[6,1]	36.414	5.559	20.591	37.239	44.583
beta3_pH[7,1]	30.549	7.987	18.532	29.764	45.115
beta3_pH[8,1]	37.328	5.675	20.212	38.982	43.865
beta3_pH[9,1]	30.774	3.794	20.774	30.638	41.221
beta3_pH[10,1]	31.830	4.422	19.163	32.817	39.042
beta3_pH[11,1]	31.647	3.189	29.322	30.426	42.443
beta3_pH[12,1]	31.197	3.085	29.268	30.262	43.078
beta3_pH[13,1]	33.772	2.225	30.930	33.256	40.740
beta3_pH[14,1]	32.578	2.190	29.933	32.078	40.056
beta3_pH[15,1]	32.701	3.712	29.731	31.393	44.477
beta3_pH[16,1]	32.795	2.802	29.920	32.013	42.504
beta3_pH[1,2]	29.995	7.987	18.441	29.105	44.887
beta3_pH[2,2]	29.874	7.823	18.535	28.784	44.849
beta3_pH[3,2]	30.055	8.009	18.448	29.208	44.825
beta3_pH[4,2]	29.718	7.851	18.509	28.412	44.632
beta3_pH[5,2]	30.030	7.980	18.529	28.914	44.855
beta3_pH[6,2]	30.164	7.956	18.562	29.350	44.921
beta3_pH[7,2]	29.934	7.971	18.420	29.033	45.063
beta3_pH[8,2]	29.702	7.973	18.424	28.474	44.840
beta3_pH[9,2]	30.062	7.873	18.501	29.167	45.059
beta3_pH[10,2]	29.900	7.881	18.409	28.864	44.829
beta3_pH[11,2]	43.416	0.184	43.106	43.401	43.796
beta3_pH[12,2]	43.190	0.187	42.951	43.142	43.697
beta3_pH[13,2]	43.865	0.150	43.469	43.906	44.040
beta3_pH[14,2]	43.304	0.207	43.051	43.248	43.807
beta3_pH[15,2]	43.428	0.199	43.107	43.407	43.834
beta3_pH[16,2]	43.502	0.188	43.165	43.498	43.846
beta3_pH[1,3]	38.855	3.477	31.777	38.790	45.251
beta3_pH[2,3]	30.168	8.016	18.408	29.166	44.864
beta3_pH[3,3]	30.054	8.126	18.498	29.043	45.070
beta3_pH[4,3]	30.106	7.899	18.397	29.336	44.927
beta3_pH[5,3]	37.084	3.995	31.239	36.574	45.102
beta3_pH[6,3]	40.312	3.654	31.757	40.752	45.596
beta3_pH[7,3]	38.013	4.330	31.336	37.784	45.471
beta3_pH[8,3]	41.496	0.256	41.056	41.496	41.945
beta3_pH[9,3]	33.501	0.559	31.799	33.586	34.341
beta3_pH[10,3]	35.845	0.771	33.561	36.019	36.846
beta3_pH[11,3]	41.862	0.783	40.255	41.857	43.342
beta3_pH[12,3]	41.736	0.393	40.967	41.743	42.521
beta3_pH[13,3]	42.875	0.947	41.030	42.881	45.058
beta3_pH[14,3]	41.087	0.587	39.882	41.106	42.205
beta3_pH[15,3]	42.746	0.658	41.265	42.850	43.816
beta3_pH[16,3]	42.969	0.735	41.334	43.076	44.196
beta0_pelagic[1]	2.222	0.134	1.955	2.223	2.482
beta0_pelagic[2]	1.473	0.122	1.241	1.471	1.707
beta0_pelagic[3]	-0.193	0.568	-1.426	-0.075	0.672
beta0_pelagic[4]	-0.393	0.819	-1.801	-0.286	0.878
beta0_pelagic[5]	1.191	0.256	0.680	1.197	1.704
beta0_pelagic[6]	1.467	0.276	0.888	1.484	1.975
beta0_pelagic[7]	1.613	0.220	1.203	1.599	2.120
beta0_pelagic[8]	1.735	0.196	1.366	1.729	2.149
beta0_pelagic[9]	2.479	0.311	1.857	2.482	3.043
beta0_pelagic[10]	2.496	0.209	2.056	2.507	2.882
beta0_pelagic[11]	-0.430	0.855	-2.436	-0.148	0.454
beta0_pelagic[12]	1.680	0.148	1.391	1.679	1.966
beta0_pelagic[13]	0.280	0.202	-0.162	0.289	0.642
beta0_pelagic[14]	-0.157	0.270	-0.780	-0.144	0.327
beta0_pelagic[15]	-0.272	0.149	-0.555	-0.271	0.018
beta0_pelagic[16]	0.201	0.293	-0.413	0.270	0.656
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	1.582	0.862	0.392	1.384	3.386
beta1_pelagic[4]	1.777	1.010	0.237	1.595	3.903
beta1_pelagic[5]	-0.071	0.309	-0.655	-0.071	0.526
beta1_pelagic[6]	-0.108	0.458	-0.874	-0.162	0.730
beta1_pelagic[7]	-0.030	0.305	-0.630	-0.032	0.567
beta1_pelagic[8]	0.010	0.272	-0.527	0.010	0.544
beta1_pelagic[9]	0.201	0.490	-0.749	0.302	0.966
beta1_pelagic[10]	0.056	0.272	-0.495	0.051	0.585
beta1_pelagic[11]	4.476	1.350	3.059	4.070	7.814
beta1_pelagic[12]	2.783	0.310	2.190	2.780	3.391
beta1_pelagic[13]	3.102	0.816	1.878	3.032	4.916
beta1_pelagic[14]	4.749	0.975	2.940	4.728	6.534
beta1_pelagic[15]	2.909	0.259	2.393	2.915	3.424
beta1_pelagic[16]	3.947	1.057	2.694	3.572	6.748
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.941	2.534	0.046	0.182	8.392
beta2_pelagic[4]	1.394	3.283	0.040	0.331	12.780
beta2_pelagic[5]	0.025	0.678	-1.389	0.013	1.494
beta2_pelagic[6]	-0.083	0.684	-1.485	-0.140	1.332
beta2_pelagic[7]	0.018	0.653	-1.321	0.029	1.403
beta2_pelagic[8]	-0.079	0.646	-1.515	-0.054	1.325
beta2_pelagic[9]	0.187	0.682	-1.296	0.263	1.480
beta2_pelagic[10]	0.005	0.631	-1.392	0.028	1.318
beta2_pelagic[11]	0.216	0.122	0.071	0.201	0.456
beta2_pelagic[12]	4.776	3.941	1.027	3.631	16.221
beta2_pelagic[13]	0.663	0.988	0.178	0.421	3.206
beta2_pelagic[14]	0.286	0.131	0.148	0.260	0.604
beta2_pelagic[15]	4.916	4.082	1.176	3.787	15.657
beta2_pelagic[16]	2.703	4.106	0.187	0.757	14.781
beta3_pelagic[1]	29.798	8.047	18.408	28.559	45.086
beta3_pelagic[2]	29.802	7.988	18.404	28.682	44.900
beta3_pelagic[3]	29.601	5.538	19.626	29.297	42.263
beta3_pelagic[4]	24.331	4.606	18.466	23.461	37.643
beta3_pelagic[5]	29.983	8.134	18.465	28.768	45.161
beta3_pelagic[6]	31.909	6.703	19.048	31.772	44.175
beta3_pelagic[7]	29.359	7.812	18.397	28.024	44.833
beta3_pelagic[8]	30.032	8.150	18.541	28.592	45.144
beta3_pelagic[9]	30.836	6.111	19.172	30.844	43.346
beta3_pelagic[10]	29.134	8.057	18.385	27.522	44.844
beta3_pelagic[11]	40.962	2.266	35.839	41.273	44.650
beta3_pelagic[12]	43.466	0.276	42.956	43.458	43.985
beta3_pelagic[13]	43.052	1.443	40.344	43.021	45.746
beta3_pelagic[14]	42.934	1.663	39.677	43.016	45.706
beta3_pelagic[15]	43.091	0.351	42.170	43.143	43.670
beta3_pelagic[16]	43.086	0.922	41.149	43.139	45.384
mu_beta0_pelagic[1]	0.687	1.034	-1.564	0.776	2.691
mu_beta0_pelagic[2]	1.810	0.385	1.042	1.813	2.558
mu_beta0_pelagic[3]	0.208	0.524	-0.862	0.232	1.203
tau_beta0_pelagic[1]	0.494	0.558	0.051	0.316	2.037
tau_beta0_pelagic[2]	2.822	3.086	0.264	1.958	9.917
tau_beta0_pelagic[3]	1.292	1.068	0.132	0.990	4.078
beta0_yellow[1]	-0.537	0.187	-0.950	-0.522	-0.216
beta0_yellow[2]	0.520	0.157	0.212	0.524	0.819
beta0_yellow[3]	-0.304	0.183	-0.703	-0.297	0.034
beta0_yellow[4]	0.815	0.286	0.078	0.863	1.209
beta0_yellow[5]	-0.313	0.356	-1.009	-0.311	0.385
beta0_yellow[6]	1.121	0.169	0.793	1.124	1.453
beta0_yellow[7]	0.992	0.160	0.684	0.992	1.313
beta0_yellow[8]	1.003	0.155	0.714	0.999	1.302
beta0_yellow[9]	0.661	0.162	0.338	0.666	0.971
beta0_yellow[10]	0.590	0.141	0.306	0.591	0.861
beta0_yellow[11]	-1.672	0.657	-2.651	-1.803	-0.177
beta0_yellow[12]	-3.640	0.442	-4.604	-3.605	-2.888
beta0_yellow[13]	-3.475	0.493	-4.509	-3.436	-2.520
beta0_yellow[14]	-1.998	0.534	-2.884	-2.046	-0.462
beta0_yellow[15]	-2.794	0.452	-3.648	-2.776	-1.846
beta0_yellow[16]	-2.310	0.424	-3.226	-2.289	-1.477
beta1_yellow[1]	0.804	1.278	0.006	0.618	2.592
beta1_yellow[2]	1.013	0.274	0.557	0.991	1.550
beta1_yellow[3]	0.697	0.339	0.212	0.681	1.182
beta1_yellow[4]	1.391	0.775	0.633	1.189	3.860
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	1.905	0.569	0.617	1.987	2.835
beta1_yellow[12]	2.434	0.455	1.666	2.379	3.424
beta1_yellow[13]	2.571	0.496	1.624	2.514	3.597
beta1_yellow[14]	2.074	0.494	0.814	2.110	2.931
beta1_yellow[15]	2.027	0.451	1.057	2.022	2.894
beta1_yellow[16]	2.070	0.436	1.196	2.060	2.982
beta2_yellow[1]	-3.911	2.819	-10.326	-3.374	-0.080
beta2_yellow[2]	-4.418	2.896	-11.023	-3.887	-0.314
beta2_yellow[3]	-3.961	2.663	-8.988	-3.715	-0.183
beta2_yellow[4]	-2.685	2.874	-9.458	-1.450	-0.096
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.671	3.095	-12.488	-4.058	-0.171
beta2_yellow[12]	-5.119	2.815	-12.280	-4.464	-1.369
beta2_yellow[13]	-5.058	2.716	-11.884	-4.412	-1.654
beta2_yellow[14]	-5.032	3.032	-12.215	-4.506	-0.489
beta2_yellow[15]	-4.638	2.821	-11.813	-3.994	-1.027
beta2_yellow[16]	-5.149	2.852	-12.134	-4.527	-1.336
beta3_yellow[1]	26.082	7.282	18.306	22.930	44.157
beta3_yellow[2]	29.132	1.543	26.963	28.847	32.869
beta3_yellow[3]	32.780	2.872	24.653	32.886	37.820
beta3_yellow[4]	29.314	3.533	22.325	28.284	36.008
beta3_yellow[5]	30.007	8.040	18.491	28.914	45.048
beta3_yellow[6]	30.060	7.836	18.502	29.142	44.806
beta3_yellow[7]	30.157	8.031	18.475	29.193	45.103
beta3_yellow[8]	30.103	8.069	18.472	29.179	44.926
beta3_yellow[9]	29.990	7.962	18.387	29.207	44.862
beta3_yellow[10]	29.929	7.837	18.496	29.090	44.780
beta3_yellow[11]	43.782	3.756	33.417	45.250	45.973
beta3_yellow[12]	43.265	0.412	42.461	43.257	44.004
beta3_yellow[13]	44.784	0.440	43.853	44.876	45.520
beta3_yellow[14]	43.888	1.895	35.342	44.157	45.777
beta3_yellow[15]	45.056	0.549	44.041	45.029	45.956
beta3_yellow[16]	44.531	0.671	43.357	44.513	45.828
mu_beta0_yellow[1]	0.125	0.555	-1.038	0.121	1.292
mu_beta0_yellow[2]	0.634	0.349	-0.150	0.662	1.269
mu_beta0_yellow[3]	-2.294	0.653	-3.308	-2.391	-0.738
tau_beta0_yellow[1]	1.848	2.709	0.090	1.161	7.239
tau_beta0_yellow[2]	3.393	4.157	0.274	2.271	13.215
tau_beta0_yellow[3]	1.361	2.143	0.089	0.869	5.454
beta0_black[1]	-0.072	0.160	-0.385	-0.070	0.249
beta0_black[2]	1.915	0.130	1.658	1.916	2.161
beta0_black[3]	1.313	0.133	1.057	1.309	1.572
beta0_black[4]	2.434	0.134	2.172	2.431	2.690
beta0_black[5]	4.687	2.131	1.906	4.176	10.027
beta0_black[6]	4.662	2.008	2.270	4.159	10.017
beta0_black[7]	3.807	1.974	1.524	3.270	9.153
beta0_black[8]	0.936	0.210	0.533	0.938	1.361
beta0_black[9]	2.609	0.234	2.157	2.607	3.070
beta0_black[10]	1.460	0.133	1.194	1.463	1.720
beta0_black[11]	3.490	0.154	3.186	3.491	3.788
beta0_black[12]	4.870	0.180	4.520	4.871	5.216
beta0_black[13]	-0.116	0.229	-0.578	-0.112	0.337
beta0_black[14]	2.855	0.157	2.552	2.854	3.157
beta0_black[15]	1.290	0.159	0.981	1.291	1.606
beta0_black[16]	4.272	0.162	3.950	4.273	4.588
beta2_black[1]	6.410	8.568	0.506	3.090	35.007
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.233	1.857	-7.299	-1.647	-0.463
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.684	1.360	39.526	41.892	43.287
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.278	0.757	37.615	39.355	40.589
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.260	0.197	-0.631	-0.260	0.128
beta4_black[2]	0.243	0.187	-0.132	0.239	0.619
beta4_black[3]	-0.928	0.193	-1.301	-0.923	-0.554
beta4_black[4]	0.427	0.217	0.013	0.421	0.861
beta4_black[5]	0.531	1.255	-1.263	0.312	3.347
beta4_black[6]	0.503	1.215	-1.209	0.299	3.586
beta4_black[7]	0.437	1.204	-1.403	0.262	3.224
beta4_black[8]	-0.219	0.314	-0.833	-0.210	0.386
beta4_black[9]	0.839	0.797	-0.219	0.673	2.869
beta4_black[10]	0.053	0.189	-0.329	0.052	0.416
beta4_black[11]	-0.700	0.217	-1.137	-0.695	-0.271
beta4_black[12]	0.171	0.326	-0.454	0.163	0.832
beta4_black[13]	-1.183	0.227	-1.637	-1.180	-0.745
beta4_black[14]	-0.182	0.233	-0.638	-0.179	0.274
beta4_black[15]	-0.888	0.218	-1.316	-0.884	-0.473
beta4_black[16]	-0.594	0.236	-1.070	-0.592	-0.140
mu_beta0_black[1]	1.283	0.945	-0.869	1.327	3.086
mu_beta0_black[2]	2.753	1.073	0.830	2.635	5.140
mu_beta0_black[3]	2.528	0.990	0.273	2.572	4.410
tau_beta0_black[1]	0.631	0.594	0.058	0.450	2.201
tau_beta0_black[2]	0.434	0.594	0.046	0.235	2.021
tau_beta0_black[3]	0.238	0.159	0.050	0.203	0.640
beta0_dsr[11]	-2.877	0.303	-3.481	-2.870	-2.322
beta0_dsr[12]	4.544	0.455	4.006	4.563	5.129
beta0_dsr[13]	-1.421	0.397	-2.381	-1.384	-0.805
beta0_dsr[14]	-3.715	0.519	-4.734	-3.686	-2.764
beta0_dsr[15]	-2.087	0.480	-3.355	-2.028	-1.338
beta0_dsr[16]	-3.018	0.360	-3.727	-3.011	-2.312
beta1_dsr[11]	4.829	0.315	4.233	4.833	5.459
beta1_dsr[12]	7.550	16.192	2.237	5.310	21.438
beta1_dsr[13]	2.972	0.507	2.325	2.901	4.513
beta1_dsr[14]	6.388	0.543	5.377	6.368	7.466
beta1_dsr[15]	4.857	2.324	2.848	3.561	10.156
beta1_dsr[16]	5.837	0.376	5.146	5.830	6.596
beta2_dsr[11]	-8.115	2.486	-14.151	-7.774	-4.309
beta2_dsr[12]	-6.604	2.889	-12.881	-6.447	-1.751
beta2_dsr[13]	-5.703	2.995	-11.909	-5.596	-0.351
beta2_dsr[14]	-5.655	2.828	-11.996	-5.337	-1.577
beta2_dsr[15]	-5.088	3.980	-11.888	-5.988	-0.070
beta2_dsr[16]	-8.085	2.989	-16.810	-7.524	-3.941
beta3_dsr[11]	43.486	0.149	43.215	43.483	43.770
beta3_dsr[12]	33.917	0.889	31.965	34.068	34.819
beta3_dsr[13]	43.240	0.454	42.496	43.200	43.933
beta3_dsr[14]	43.371	0.240	43.077	43.309	43.960
beta3_dsr[15]	40.157	4.876	31.099	43.359	43.833
beta3_dsr[16]	43.436	0.160	43.156	43.426	43.762
beta4_dsr[11]	0.576	0.219	0.162	0.572	1.014
beta4_dsr[12]	0.260	0.435	-0.592	0.252	1.142
beta4_dsr[13]	-0.166	0.220	-0.611	-0.161	0.265
beta4_dsr[14]	0.149	0.252	-0.350	0.152	0.639
beta4_dsr[15]	0.717	0.218	0.304	0.712	1.158
beta4_dsr[16]	0.157	0.228	-0.305	0.162	0.599
beta0_slope[11]	-1.848	0.149	-2.142	-1.850	-1.552
beta0_slope[12]	-4.469	0.254	-4.968	-4.466	-3.980
beta0_slope[13]	-1.335	0.175	-1.714	-1.326	-1.020
beta0_slope[14]	-2.674	0.168	-3.011	-2.676	-2.337
beta0_slope[15]	-1.346	0.148	-1.628	-1.346	-1.045
beta0_slope[16]	-2.732	0.158	-3.046	-2.730	-2.426
beta1_slope[11]	4.488	0.224	4.056	4.485	4.921
beta1_slope[12]	3.983	0.459	3.076	3.974	4.909
beta1_slope[13]	2.701	0.426	2.200	2.637	3.824
beta1_slope[14]	6.311	0.411	5.504	6.312	7.110
beta1_slope[15]	3.009	0.209	2.598	3.003	3.429
beta1_slope[16]	5.277	0.284	4.708	5.273	5.847
beta2_slope[11]	8.510	2.238	4.974	8.195	13.624
beta2_slope[12]	6.537	2.829	1.119	6.602	12.497
beta2_slope[13]	5.460	2.993	0.463	5.474	11.559
beta2_slope[14]	6.414	2.415	2.417	6.283	11.645
beta2_slope[15]	8.159	2.342	4.414	7.846	13.767
beta2_slope[16]	7.700	2.114	4.341	7.402	12.635
beta3_slope[11]	43.461	0.136	43.215	43.457	43.724
beta3_slope[12]	43.352	0.278	42.868	43.313	43.908
beta3_slope[13]	43.461	0.376	42.960	43.406	44.039
beta3_slope[14]	43.262	0.132	43.093	43.230	43.590
beta3_slope[15]	43.493	0.162	43.196	43.489	43.798
beta3_slope[16]	43.372	0.141	43.154	43.353	43.693
beta4_slope[11]	-0.731	0.166	-1.058	-0.731	-0.412
beta4_slope[12]	-1.156	0.469	-2.199	-1.116	-0.368
beta4_slope[13]	0.085	0.164	-0.235	0.083	0.411
beta4_slope[14]	-0.086	0.199	-0.474	-0.085	0.319
beta4_slope[15]	-0.762	0.156	-1.072	-0.760	-0.456
beta4_slope[16]	-0.161	0.175	-0.509	-0.160	0.186
sigma_H[1]	0.199	0.054	0.104	0.196	0.317
sigma_H[2]	0.172	0.030	0.117	0.170	0.236
sigma_H[3]	0.196	0.042	0.119	0.193	0.283
sigma_H[4]	0.409	0.075	0.285	0.402	0.581
sigma_H[5]	0.991	0.213	0.593	0.983	1.439
sigma_H[6]	0.384	0.207	0.028	0.378	0.819
sigma_H[7]	0.304	0.063	0.208	0.296	0.448
sigma_H[8]	0.420	0.102	0.269	0.406	0.658
sigma_H[9]	0.510	0.125	0.323	0.491	0.797
sigma_H[10]	0.214	0.044	0.140	0.209	0.313
sigma_H[11]	0.275	0.044	0.201	0.272	0.373
sigma_H[12]	0.439	0.168	0.207	0.415	0.778
sigma_H[13]	0.211	0.038	0.142	0.208	0.294
sigma_H[14]	0.495	0.096	0.329	0.489	0.703
sigma_H[15]	0.246	0.041	0.180	0.242	0.341
sigma_H[16]	0.231	0.045	0.158	0.226	0.334
lambda_H[1]	3.156	4.507	0.180	1.778	13.945
lambda_H[2]	8.607	8.067	0.759	6.305	30.622
lambda_H[3]	6.994	9.919	0.305	3.503	33.833
lambda_H[4]	0.007	0.005	0.001	0.005	0.018
lambda_H[5]	3.426	6.724	0.028	0.849	26.270
lambda_H[6]	8.323	15.769	0.008	1.504	52.451
lambda_H[7]	0.013	0.010	0.002	0.010	0.038
lambda_H[8]	7.535	10.087	0.001	4.152	37.274
lambda_H[9]	0.016	0.011	0.003	0.013	0.045
lambda_H[10]	0.303	0.498	0.032	0.193	1.167
lambda_H[11]	0.274	0.367	0.011	0.144	1.269
lambda_H[12]	4.979	6.501	0.174	2.772	23.068
lambda_H[13]	3.852	3.798	0.267	2.823	13.341
lambda_H[14]	3.294	3.820	0.238	2.132	13.329
lambda_H[15]	0.034	0.322	0.004	0.017	0.107
lambda_H[16]	1.585	2.747	0.056	0.693	9.792
mu_lambda_H[1]	4.393	1.928	1.191	4.192	8.551
mu_lambda_H[2]	3.822	1.953	0.575	3.692	7.943
mu_lambda_H[3]	3.607	1.864	0.879	3.358	7.848
sigma_lambda_H[1]	8.708	4.355	2.022	8.025	18.230
sigma_lambda_H[2]	8.384	4.645	1.011	7.972	18.255
sigma_lambda_H[3]	6.390	3.963	1.097	5.577	16.526
beta_H[1,1]	6.912	1.017	4.486	7.056	8.502
beta_H[2,1]	9.867	0.494	8.827	9.896	10.738
beta_H[3,1]	8.011	0.761	6.204	8.097	9.225
beta_H[4,1]	9.740	7.869	-6.383	10.032	24.716
beta_H[5,1]	0.184	2.452	-4.845	0.404	4.409
beta_H[6,1]	3.316	3.894	-7.380	4.735	7.573
beta_H[7,1]	0.574	5.760	-11.709	0.856	11.202
beta_H[8,1]	4.518	12.465	-2.444	1.359	51.446
beta_H[9,1]	13.081	5.642	1.735	13.061	24.424
beta_H[10,1]	7.117	1.726	3.533	7.180	10.375
beta_H[11,1]	5.271	3.517	-2.743	6.126	10.037
beta_H[12,1]	2.615	1.032	0.761	2.570	4.821
beta_H[13,1]	9.045	0.877	7.213	9.102	10.526
beta_H[14,1]	2.177	1.007	0.095	2.175	4.159
beta_H[15,1]	-5.963	3.858	-12.949	-6.143	2.403
beta_H[16,1]	3.387	2.230	-0.535	3.231	8.269
beta_H[1,2]	7.914	0.241	7.411	7.921	8.359
beta_H[2,2]	10.034	0.136	9.766	10.033	10.300
beta_H[3,2]	8.958	0.192	8.585	8.956	9.333
beta_H[4,2]	3.468	1.485	0.665	3.420	6.461
beta_H[5,2]	1.969	0.992	-0.023	2.002	3.863
beta_H[6,2]	5.806	1.026	3.405	5.987	7.381
beta_H[7,2]	2.643	1.101	0.669	2.596	4.941
beta_H[8,2]	2.271	2.955	-8.464	3.101	4.247
beta_H[9,2]	3.409	1.129	1.266	3.367	5.735
beta_H[10,2]	8.178	0.353	7.453	8.191	8.841
beta_H[11,2]	9.747	0.639	8.824	9.624	11.222
beta_H[12,2]	3.964	0.372	3.266	3.957	4.736
beta_H[13,2]	9.127	0.248	8.684	9.116	9.623
beta_H[14,2]	4.028	0.353	3.351	4.023	4.722
beta_H[15,2]	11.345	0.689	9.927	11.382	12.593
beta_H[16,2]	4.790	0.891	3.098	4.775	6.614
beta_H[1,3]	8.487	0.243	8.049	8.470	8.981
beta_H[2,3]	10.088	0.121	9.857	10.085	10.329
beta_H[3,3]	9.622	0.158	9.313	9.622	9.936
beta_H[4,3]	-2.386	0.897	-4.153	-2.377	-0.640
beta_H[5,3]	3.939	0.631	2.680	3.941	5.181
beta_H[6,3]	7.967	1.180	6.400	7.548	10.588
beta_H[7,3]	-2.750	0.682	-4.095	-2.733	-1.471
beta_H[8,3]	5.649	1.379	4.683	5.244	10.524
beta_H[9,3]	-2.683	0.809	-4.253	-2.691	-1.105
beta_H[10,3]	8.729	0.286	8.190	8.721	9.293
beta_H[11,3]	8.564	0.291	7.912	8.589	9.064
beta_H[12,3]	5.275	0.316	4.562	5.312	5.811
beta_H[13,3]	8.893	0.190	8.509	8.895	9.266
beta_H[14,3]	5.754	0.274	5.171	5.768	6.269
beta_H[15,3]	10.393	0.319	9.775	10.387	11.012
beta_H[16,3]	6.620	0.698	5.261	6.612	7.931
beta_H[1,4]	8.278	0.179	7.898	8.290	8.588
beta_H[2,4]	10.149	0.124	9.880	10.158	10.381
beta_H[3,4]	10.136	0.156	9.793	10.149	10.401
beta_H[4,4]	11.795	0.447	10.896	11.799	12.651
beta_H[5,4]	5.644	0.819	4.378	5.531	7.536
beta_H[6,4]	7.167	0.887	5.098	7.440	8.367
beta_H[7,4]	8.289	0.351	7.594	8.286	8.996
beta_H[8,4]	6.600	0.519	4.859	6.715	7.157
beta_H[9,4]	7.160	0.474	6.262	7.154	8.137
beta_H[10,4]	7.746	0.238	7.312	7.739	8.251
beta_H[11,4]	9.407	0.201	9.021	9.408	9.803
beta_H[12,4]	7.147	0.210	6.747	7.145	7.554
beta_H[13,4]	9.071	0.151	8.780	9.069	9.367
beta_H[14,4]	7.752	0.223	7.315	7.752	8.189
beta_H[15,4]	9.492	0.244	9.021	9.495	9.968
beta_H[16,4]	9.309	0.226	8.916	9.294	9.780
beta_H[1,5]	8.992	0.142	8.705	8.997	9.259
beta_H[2,5]	10.786	0.096	10.608	10.782	10.982
beta_H[3,5]	10.904	0.165	10.614	10.894	11.256
beta_H[4,5]	8.384	0.451	7.531	8.372	9.308
beta_H[5,5]	5.369	0.649	3.753	5.449	6.411
beta_H[6,5]	8.802	0.610	7.922	8.660	10.279
beta_H[7,5]	6.771	0.342	6.087	6.772	7.427
beta_H[8,5]	8.313	0.405	7.864	8.228	9.697
beta_H[9,5]	8.213	0.473	7.280	8.214	9.139
beta_H[10,5]	10.093	0.229	9.617	10.097	10.528
beta_H[11,5]	11.501	0.220	11.074	11.499	11.936
beta_H[12,5]	8.490	0.195	8.114	8.490	8.880
beta_H[13,5]	10.015	0.131	9.755	10.016	10.281
beta_H[14,5]	9.206	0.224	8.775	9.194	9.669
beta_H[15,5]	11.169	0.251	10.676	11.175	11.670
beta_H[16,5]	9.940	0.168	9.601	9.946	10.260
beta_H[1,6]	10.182	0.188	9.855	10.167	10.598
beta_H[2,6]	11.513	0.109	11.302	11.512	11.731
beta_H[3,6]	10.825	0.159	10.485	10.835	11.118
beta_H[4,6]	12.877	0.799	11.273	12.891	14.430
beta_H[5,6]	5.939	0.642	4.744	5.929	7.233
beta_H[6,6]	8.839	0.669	7.065	8.963	9.809
beta_H[7,6]	9.881	0.565	8.772	9.885	11.000
beta_H[8,6]	9.406	0.563	7.491	9.520	9.990
beta_H[9,6]	8.443	0.778	6.920	8.420	10.006
beta_H[10,6]	9.517	0.320	8.810	9.538	10.101
beta_H[11,6]	10.835	0.336	10.110	10.865	11.431
beta_H[12,6]	9.375	0.248	8.899	9.363	9.904
beta_H[13,6]	11.050	0.158	10.754	11.043	11.379
beta_H[14,6]	9.814	0.293	9.211	9.816	10.369
beta_H[15,6]	10.845	0.436	9.944	10.844	11.698
beta_H[16,6]	10.581	0.221	10.118	10.591	11.006
beta_H[1,7]	10.862	0.865	8.799	10.960	12.283
beta_H[2,7]	12.214	0.429	11.313	12.225	13.036
beta_H[3,7]	10.607	0.649	9.153	10.677	11.689
beta_H[4,7]	2.439	4.050	-5.476	2.369	10.517
beta_H[5,7]	6.567	1.952	3.225	6.461	10.947
beta_H[6,7]	9.627	2.413	4.587	9.583	15.570
beta_H[7,7]	10.576	2.850	4.977	10.579	16.355
beta_H[8,7]	11.426	2.306	9.315	10.959	19.473
beta_H[9,7]	4.421	3.957	-3.567	4.496	12.186
beta_H[10,7]	9.828	1.470	7.113	9.761	12.917
beta_H[11,7]	10.903	1.657	7.775	10.800	14.451
beta_H[12,7]	9.999	0.943	7.831	10.089	11.605
beta_H[13,7]	11.679	0.716	10.061	11.769	12.812
beta_H[14,7]	10.379	0.914	8.461	10.429	11.992
beta_H[15,7]	11.948	2.246	7.386	11.984	16.539
beta_H[16,7]	12.084	1.125	10.310	11.893	14.725
beta0_H[1]	8.916	12.462	-16.446	8.893	35.148
beta0_H[2]	10.603	6.587	-2.317	10.613	23.911
beta0_H[3]	9.787	9.296	-10.437	9.932	29.332
beta0_H[4]	7.175	186.216	-369.203	6.818	382.213
beta0_H[5]	3.849	26.714	-49.735	4.256	60.459
beta0_H[6]	8.466	46.053	-94.537	7.885	117.487
beta0_H[7]	0.011	132.986	-283.829	0.986	262.318
beta0_H[8]	6.974	107.996	-186.362	6.608	212.471
beta0_H[9]	4.698	122.531	-242.786	3.021	259.068
beta0_H[10]	8.421	33.986	-61.288	8.750	75.787
beta0_H[11]	9.578	48.293	-94.138	10.390	109.599
beta0_H[12]	6.570	11.586	-17.001	6.659	29.674
beta0_H[13]	9.997	10.259	-10.575	10.116	29.015
beta0_H[14]	7.041	11.185	-14.100	7.150	29.437
beta0_H[15]	9.915	102.523	-194.534	8.924	218.036
beta0_H[16]	8.786	21.292	-34.024	8.077	57.011